Changes to retirement savings are coming, the House's top tax writer said Wednesday, despite a tweet earlier this week from President Donald Trump that there would be no changes to 401(k)s.

“We think, in tax reform, we can create incentives for Americans to save more and save sooner, which can help,” Ways and Means Chairman Kevin Brady (R-Texas) told reporters. “So we are exploring a number of ideas in those areas.”

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Separately, Senate Finance Chairman Orrin Hatch (R-Utah), said he was "open to looking at anything."

The comments indicate the rift over the issue is far from settled as House Republicans prepare to release their tax reform bill next week. Ways and Means Republicans spent a good chunk of a four-hour closed meeting Wednesday discussing 401(k)s, according to someone familiar with the private deliberations.

Trump, who blasted out his tweet on Monday after news reports about the issue, continued to warn against tampering with 401(k)s.

“I wanted to end that quickly," he told reporters Wednesday. "401(k)s, to me, are very important, and they’re important because that’s one of the great benefits to the middle class. I didn’t want that to go too far. That’s why I ended it very quickly.”

Asked about Brady's comments that the issue could still be on the table, Trump said: “Well, maybe it is, and maybe we’ll use it as negotiating. But trust me. That’s one of the great things. You know, there are certain elements of deals you don’t wanna negotiate with. 401(k)s — and Kevin knows it, and I think Kevin Brady is fantastic, but he knows how important 401(k)s are.”

GOP lawmakers drafting a tax overhaul have considered lowering the cap on how much employees can contribute to the employer-sponsored savings plans and steering additional savings toward plans that would tax contributions up-front, rather than when savers withdraw money as is currently the practice with 401(k)s.

“We think we can do better," Brady told reporters at a Christian Science Monitor breakfast.

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He declined to discuss specifics. But one idea being discussed, according to sources who deal with retirement savings issues, would make more people eligible for a separate saver’s tax break and make it worth more to sweeten retirement savings, even if people are forced to do more of it with after-tax contributions to employer-sponsored plans like 401(k)s rather than pre-tax money.

Data show that half of those who use 401(k)s and other retirement savings vehicles like individual retirement accounts contribute $200 or less per month, Brady said.

“We want Americans to save more and earlier in their life,” he said.

But when reports of the 401(k) discussions surfaced last week, Trump tried to squelch it.

"There will be NO change to your 401(k). This has always been a great and popular middle class tax break that works, and it stays!" he wrote Monday on Twitter.

But Brady said talks on the issue were ongoing.

“We are continuing discussions with the president, all focused on saving more, saving sooner,” Brady said.

Earlier this week, when Hatch was asked about Trump's tweet, he said: “Keep in mind. He can make his moves but we’re going to do things up here that might be a little bit different. That may be one where we have to say, ‘We disagree,’ but we’ll see, we’ll see."

Republican leaders are searching for ways to fund some of the tax cuts they want to pass, and 401(k) changes have been eyed at several points during the process. But the White House is sensitive to anything that could be construed as dinging the middle class.

Some GOP lawmakers are also wary of changing 401(k)s.

“I’m not in favor of it. It just goes against the hardworking middle-income wage earners," said Rep. Mark Meadows (R-N.C.), who heads the staunchly conservative House Freedom Caucus. "I don’t think that’s a good thing to be doing."

Rep. Warren Davidson (R-Ohio), another Freedom Caucus member, said, “I think it’s a really bad idea. You could say maybe the current structure hasn’t worked as well as was hoped for, but making it harder for people to save seems like the wrong direction.”

On another major tax reform dispute, Brady said he expects a compromise on the state and local tax deduction to be announced before a tax overhaul bill is released.

“I do expect to reach an agreement with our high-tax lawmakers,” he said.

A group of Republicans who represent high-tax districts in New York and New Jersey are rebelling against a plan by Republican leaders and the Trump administration to end the federal deduction taxpayers can take for the state and local taxes they pay, including property taxes. Several have threatened to vote against the budget — which is crucial to the GOP’s tax plans — on Thursday unless the leaders retreat from their plans.

Brady wouldn’t elaborate on what kind of deal Republicans are considering. Lawmakers have floated several ideas, including an income threshold for who could keep the current benefit or changing the deduction to a tax credit.

However, business deductions for state and local taxes won’t get eliminated, Brady said.

“It is a tiny part of business expenses,” he said.

No decision has been made yet on a top income tax bracket for individuals, Brady said. Sensitive to charges that their tax plan would mostly benefit the wealthy, Republicans are weighing strategies like adding a fourth bracket for high-income earners to the three brackets they have already proposed.

The committee is also still undecided what income levels would fit into those three brackets, Brady said.

He said the committee is considering an issue dear to U.S. citizens living abroad — letting them pay taxes only where they live — though no decision has been made.

When Brady was asked about Trump’s heated feuds with some Republican lawmakers, notably Sens. Bob Corker (R-Tenn.) and Jeff Flake (R-Ariz.), he said he had a good relationship with Trump.